Uma abordagem algébrica para solução de EDO’s lineares com coeficientes constantes

Abstract

The study of differential equations is an extensive field of mathematics having numerous practical applications in medicine, engineering, chemistry, biology and other fields of knowledge. In order to introduce a purely algebraic, flexible and elegant approach to the well-known classical theory of linear ordinary differential equations with constant coefficients, in this work we will study the ring of symmetric functions and formal power series and apply these concepts in the development of an algebraic method with which we will be able to obtain the solution of an initial value problem considering that these equations have constant coefficients in any Q-algebra. The generality of the method presented here allows the development of efficient computational implementations to obtain good representations of the solutions, independently of the order of the equation.